Uncertainty Quantification of Object Boundaries Extracted from Spatial Point Pattern Images

Oregon Convention Center 

Identifying the boundaries of irregular regions of extended astronomical emission poses significant challenges due to their complex features and background contamination. In high-energy astrophysics, one strategy is to segment event lists by using algorithms that aggregate photons into distinct spatial clusters, typically based on their two-dimensional sky coordinates. \citet{Fan_2023}, for example, introduced ``Seeded Region Growing on a Graph'' (\srgong), which combines a likeihood-based representation of an inhomogenious Poisson process with flexible non-parametric representation of the segments to derive maximum likelihood estimates of the segments, their number, and their Poisson rates. In this paper, we first introduce several modifications to \srgong\ to enhance its performance and stability under low Signal-to-Noise (S/N) conditions. In addition, we introduce \uqbose, a new set of algorithms and statistical methods that quantify the uncertainty associated with a segment boundary. This is accomplished via a parameterization of the boundary derived using Fourier Descriptors along with spatial bootstrap techniques, including both parametric and non-parametric methods, to effectively assess the uncertainty of the parameter estimates. We also construct a small-size global confidence region for the true object shape and validate the overall \uqbose\ procedure through comparisons between the empirical coverage rate of the global confidence region with its theoretical bounds under various numerical experiment scenarios.